Professor Daniel Paulusma's Outputs (311)

A Reconfigurations Analogue of Brooks’ Theorem (2014)
Presentation / Conference Contribution
Feghali, C., Johnson, M., & Paulusma, D. (2014, December). A Reconfigurations Analogue of Brooks’ Theorem. Presented at 39th International Symposium, MFCS 2014, Budapest, Hungary

Let G be a simple undirected graph on n vertices with maximum degree Δ. Brooks’ Theorem states that G has a Δ-colouring unless G is a complete graph, or a cycle with an odd number of vertices. To recolour G is to obtain a new proper colouring by chan... Read More about A Reconfigurations Analogue of Brooks’ Theorem.

Editing to Eulerian Graphs (2014)
Presentation / Conference Contribution
Dabrowski, K. K., Golovach, P. A., Hof, V. P., & Paulusma, D. (2014, December). Editing to Eulerian Graphs. Presented at 34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014), Budapest, Hungary

We investigate the problem of modifying a graph into a connected graph in which the degree of each vertex satisfies a prescribed parity constraint. Let ea, ed and vd denote the operations edge addition, edge deletion and vertex deletion respectively.... Read More about Editing to Eulerian Graphs.

Classifying the Clique-Width of H-Free Bipartite Graphs (2014)
Presentation / Conference Contribution
Dabrowski, K. K., & Paulusma, D. (2014, December). Classifying the Clique-Width of H-Free Bipartite Graphs. Presented at 20th International Conference, COCOON 2014, Atlanta, GA, USA

Let G be a bipartite graph, and let H be a bipartite graph with a fixed bipartition (B H ,W H ). We consider three different, natural ways of forbidding H as an induced subgraph in G. First, G is H-free if it does not contain H as an induced subgraph... Read More about Classifying the Clique-Width of H-Free Bipartite Graphs.

Induced Disjoint Paths in Circular-Arc Graphs in Linear Time (2014)
Presentation / Conference Contribution
Golovach, P., Paulusma, D., & van Leeuwen, E. (2014, December). Induced Disjoint Paths in Circular-Arc Graphs in Linear Time. Presented at 40th International Workshop, WG 2014, Nouan-le-Fuzelier, France

The Induced Disjoint Paths problem is to test whether a graph G with k distinct pairs of vertices (si,ti) contains paths P1,…,Pk such that Pi connects si and ti for i=1,…,k, and Pi and Pj have neither common vertices nor adjacent vertices (except per... Read More about Induced Disjoint Paths in Circular-Arc Graphs in Linear Time.

Narrowing the Complexity Gap for Colouring (C_s,P_t)-Free Graphs (2014)
Presentation / Conference Contribution
Huang, S., Johnson, M., & Paulusma, D. (2014, December). Narrowing the Complexity Gap for Colouring (C_s,P_t)-Free Graphs. Presented at 10th International Conference, AAIM 2014, Vancouver, BC, Canada

Let k be a positive integer. The k-Colouring problem is to decide whether a graph has a k-colouring. The k-Precolouring Extension problem is to decide whether a colouring of a subset of a graph’s vertex set can be extended to a k-colouring of the who... Read More about Narrowing the Complexity Gap for Colouring (C_s,P_t)-Free Graphs.

Forbidden Induced Subgraphs and the Price of Connectivity for Feedback Vertex Set (2014)
Presentation / Conference Contribution
Belmonte, R., Hof, V. '. P., Kaminski, M., & Paulusma, D. (2014, December). Forbidden Induced Subgraphs and the Price of Connectivity for Feedback Vertex Set. Presented at 39th International Symposium, MFCS 2014, Budapest, Hungary

Let fvs(G) and cfvs(G) denote the cardinalities of a minimum feedback vertex set and a minimum connected feedback vertex set of a graph G, respectively. For a graph class G, the price of connectivity for feedback vertex set (poc-fvs) for G is defined... Read More about Forbidden Induced Subgraphs and the Price of Connectivity for Feedback Vertex Set.

Modifying a Graph Using Vertex Elimination (2013)
Journal Article
Golovach, P., Heggernes, P., Hof, V. '. P., Manne, F., Paulusma, D., & Pilipczuk, M. (2015). Modifying a Graph Using Vertex Elimination. Algorithmica, 72(1), 99-125. https://doi.org/10.1007/s00453-013-9848-2

Vertex elimination is a graph operation that turns the neighborhood of a vertex into a clique and removes the vertex itself. It has widely known applications within sparse matrix computations. We define the Elimination problem as follows: given two g... Read More about Modifying a Graph Using Vertex Elimination.

Characterizing graphs of small carving-width (2013)
Journal Article
Belmonte, R., Hof, V. '. P., Kaminski, M., Paulusma, D., & Thilikos, D. (2013). Characterizing graphs of small carving-width. Discrete Applied Mathematics, 161(13-14), 1888-1893. https://doi.org/10.1016/j.dam.2013.02.036

We characterize all graphs that have carving-width at most k for k=1,2,3. In particular, we show that a graph has carving-width at most 3 if and only if it has maximum degree at most 3 and treewidth at most 2. This enables us to identify the immersio... Read More about Characterizing graphs of small carving-width.

Detecting induced minors in AT-free graphs (2013)
Journal Article
Golovach, P., Kratsch, D., & Paulusma, D. (2013). Detecting induced minors in AT-free graphs. Theoretical Computer Science, 482, 20-32. https://doi.org/10.1016/j.tcs.2013.02.029

The Induced Minor problem is that of testing whether a graph G can be modified into a graph H by a sequence of vertex deletions and edge contractions. If only edge contractions are permitted, we obtain the Contractibility problem. We prove that Induc... Read More about Detecting induced minors in AT-free graphs.

List Coloring in the Absence of a Linear Forest (2013)
Journal Article
Couturier, J., Golovach, P., Kratsch, D., & Paulusma, D. (2015). List Coloring in the Absence of a Linear Forest. Algorithmica, 71(1), 21-35. https://doi.org/10.1007/s00453-013-9777-0

The k-Coloring problem is to decide whether a graph can be colored with at most k colors such that no two adjacent vertices receive the same color. The Listk-Coloring problem requires in addition that every vertex u must receive a color from some giv... Read More about List Coloring in the Absence of a Linear Forest.

Increasing the minimum degree of a graph by contractions (2013)
Journal Article
Golovach, P., Kaminski, M., Paulusma, D., & Thilikos, D. (2013). Increasing the minimum degree of a graph by contractions. Theoretical Computer Science, 481, 74-84. https://doi.org/10.1016/j.tcs.2013.02.030

The Degree Contractibility problem is to test whether a given graph G can be modified to a graph of minimum degree at least d by using at most k contractions. We prove the following three results. First, Degree Contractibility is NP-complete even whe... Read More about Increasing the minimum degree of a graph by contractions.

Satisfiability of acyclic and almost acyclic CNF formulas (2013)
Journal Article
Ordyniak, S., Paulusma, D., & Szeider, S. (2013). Satisfiability of acyclic and almost acyclic CNF formulas. Theoretical Computer Science, 481, 85-99. https://doi.org/10.1016/j.tcs.2012.12.039

We show that the Satisfiability (SAT) problem for CNF formulas with ββ-acyclic hypergraphs can be solved in polynomial time by using a special type of Davis–Putnam resolution in which each resolvent is a subset of a parent clause. We extend this clas... Read More about Satisfiability of acyclic and almost acyclic CNF formulas.

Three complexity results on coloring Pk-free graphs (2013)
Journal Article
Broersma, H., Fomin, F., Golovach, P., & Paulusma, D. (2013). Three complexity results on coloring Pk-free graphs. European Journal of Combinatorics, 34(3), 609-619. https://doi.org/10.1016/j.ejc.2011.12.008

We prove three complexity results on vertex coloring problems restricted to PkPk-free graphs, i.e., graphs that do not contain a path on kk vertices as an induced subgraph. First of all, we show that the pre-coloring extension version of 5-coloring r... Read More about Three complexity results on coloring Pk-free graphs.

Obtaining planarity by contracting few edges (2013)
Journal Article
Golovach, P., van 't Hof, P., & Paulusma, D. (2013). Obtaining planarity by contracting few edges. Theoretical Computer Science, 476, 38-46. https://doi.org/10.1016/j.tcs.2012.12.041

The Planar Contraction problem is to test whether a given graph can be made planar by using at most kk edge contractions. This problem is known to be NP-complete. We show that it is fixed-parameter tractable when parameterized by kk.

Choosability on H-free graphs (2013)
Journal Article
Golovach, P., Heggernes, P., van 't Hof, P., & Paulusma, D. (2013). Choosability on H-free graphs. Information Processing Letters, 113(4), 107-110. https://doi.org/10.1016/j.ipl.2012.12.003

A graph is H-free if it has no induced subgraph isomorphic to H. We determine the computational complexity of the Choosability problem restricted to H-free graphs for every graph H that does not belong to {K1,3,P1+P2,P1+P3,P4}{K1,3,P1+P2,P1+P3,P4}. W... Read More about Choosability on H-free graphs.

A note on contracting claw-free graphs (2013)
Journal Article
Fiala, J., Kaminski, M., & Paulusma, D. (2013). A note on contracting claw-free graphs. Discrete Mathematics & Theoretical Computer Science, 15(2), 223-232

A graph containment problem is to decide whether one graph called the host graph can be modified into some other graph called the target graph by using a number of specified graph operations. We consider edge deletions, edge contractions, vertex dele... Read More about A note on contracting claw-free graphs.

4-Coloring H-free graphs when H is small (2013)
Journal Article
Golovach, P., Paulusma, D., & Song, J. (2013). 4-Coloring H-free graphs when H is small. Discrete Applied Mathematics, 161(1-2), 140-150. https://doi.org/10.1016/j.dam.2012.08.022

The kk-Coloring problem is to test whether a graph can be colored with at most kk colors such that no two adjacent vertices receive the same color. If a graph GG does not contain a graph HH as an induced subgraph, then GG is called HH-free. For any f... Read More about 4-Coloring H-free graphs when H is small.

Exact algorithms for finding longest cycles in claw-free graphs (2013)
Journal Article
Broersma, H., Fomin, F., Hof van 't, P., & Paulusma, D. (2013). Exact algorithms for finding longest cycles in claw-free graphs. Algorithmica, 65(1), 129 -145. https://doi.org/10.1007/s00453-011-9576-4

The Hamiltonian Cycle problem is the problem of deciding whether an n-vertex graph G has a cycle passing through all vertices of G. This problem is a classic NP-complete problem. Finding an exact algorithm that solves it in O*(an)(n) time for some co... Read More about Exact algorithms for finding longest cycles in claw-free graphs.

Locally Constrained Homomorphisms on Graphs of Bounded Treewidth and Bounded Degree (2013)
Presentation / Conference Contribution
Chaplick, S., Fiala, J., Hof, V. '. P., Paulusma, D., & Tesar, M. (2013, December). Locally Constrained Homomorphisms on Graphs of Bounded Treewidth and Bounded Degree. Presented at Liverpool, UK, 19th International Symposium, FCT 2013

A homomorphism from a graph G to a graph H is locally bijective, surjective, or injective if its restriction to the neighborhood of every vertex of G is bijective, surjective, or injective, respectively. We prove that the problems of testing whether... Read More about Locally Constrained Homomorphisms on Graphs of Bounded Treewidth and Bounded Degree.

Parameterized Complexity of Two Edge Contraction Problems with Degree Constraints (2013)
Presentation / Conference Contribution
Belmonte, R., Golovach, P., Hof, V. '. P., & Paulusma, D. (2013, December). Parameterized Complexity of Two Edge Contraction Problems with Degree Constraints. Presented at 8th International Symposium, IPEC 2013, Sophia Antipolis, France

Motivated by recent results of Mathieson and Szeider (J. Comput. Syst. Sci. 78(1): 179–191, 2012), we study two graph modification problems where the goal is to obtain a graph whose vertices satisfy certain degree constraints. The Regular Contraction... Read More about Parameterized Complexity of Two Edge Contraction Problems with Degree Constraints.